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As long as no one can provide references, what's the difference between Classical and Phenomenological thermodynamics, I sincerely believe them to be synonyms. -- Pjacobi 14:59, 3 November 2006 (UTC) reply

I see you want to merge phenomenological thermodynamics and equilibrium thermodynamics into this article. Other others have wanted to merge statistical thermodynamics and statistical mechanics into one one article. With the latter case, the consensus was to leave them separate. As to this suggestion, I am working to build a decent article on each topic in thermodynamics. The following list gives a rough outline as to when the major branches of thermodynamics came into inception:

• Thermochemistry - 1780s
• Classical thermodynamics - 1824
• Phenomenological thermodynamics
• Chemical thermodynamics - 1876
• Statistical thermodynamics - c. 1880s
• Equilibrium thermodynamics
• Engineering thermodynamics
• Psychodynamics - c. 1920s
• Chemical engineering thermodynamics - c. 1940s
• Non-equilibrium thermodynamics - 1941
• Small systems thermodynamics - 1960s
• Biological thermodynamics - 1957
• Ecosystem thermodynamics - 1959
• Relativistic thermodynamics - 1965
• Quantum thermodynamics - 1968
• Molecular thermodynamics - 1969
• Thermoeconomics - c. 1970s
• Black hole thermodynamics - c. 1970s
• Geological thermodynamics - c. 1970s
• Biological evolution thermodynamics - 1978
• Geochemical thermodynamics - c. 1980s
• Atmospheric thermodynamics - c. 1980s
• Natural systems thermodynamics - 1990s
• Supramolecular thermodynamics - 1990s
• Earthquake thermodynamics - 2000
• Drug-receptor thermodynamics - 2001
• Pharmaceutical systems thermodynamics – 2002

Please be patient, it is not easy the subtle difference between each of these subjects. Yet, there are full textbooks on each. Hence, this is a work in progress; each topic has its own subtle agenda. Thanks: -- Sadi Carnot 15:19, 2 December 2006 (UTC) reply

New user 128.175.75.147 dumped all this stuff into the main page as is:

The First Law of Thermodynamics essentially comes from an energy balance upon systems (whether they are open to the environment or isolated from it). An overall (but simplified) balance comes as such (neglecting kinetic and potential energy):

(dU/dt) = sum(Ni Hi) + Q + Ws - P(dV/dt) Where U represents the internal energy of a system, Ni represents the mole/mass of a particular input/output to the system, Hi represents the total enthalpy of the corresponding inlet/outlet of stream i, Q represents the total heat flux into/out of the system, Ws represents the shaft work performed on/by the system, P is the pressure of the system, V is the specific volume of the system, and t represents time. The equation above can be applied to either open or closed systems: since many open systems are generally at steady state (i.e. not time dependent) the time derivative terms are cancelled, otherwise with a closed system the mass flux into/out of the system is generally zero (because it is isolated from the environment). The Second Law of Thermodynamics comes about from the development of the relationship known as entropy. Entropy can be crudely represented as a type of chaos/disorder introduced into a system, and typically throughout the universe entropy will always be increasing. The Second Law essentially refers to the generation of entropy always being greater than (or equal to) zero. This relationship physically comes about in the following equation (neglecting kinetic and potential energy): (dS/dt) = sum(Ni Si) - Q/T + Sgen Where t, Q, Ni remain the same as before, T represents temperature, S is the entropy of the system (for closed systems), Si is the total entropy of the inlet/outlet represented by i, and Sgen is the entropy generation term which is greater than or equal to zero. In the classroom or for best estimates of processes at their maximum ideality, the Sgen term is assumed as zero (but this is usually always greater than zero, because there hardly exists a truly ideal process in current technology).

In further work of thermodynamics, several quantities have been developed to represent different types of energy that can be described by systems, they are: internal energy (U), enthalpy (H), Helmholtz energy (A), and Gibbs energy (G). The quantities are related as follows:

H = U + PV,

A = U - TS,

G = H - TS,

(where P = pressure, V = specific volume, T = temperature, and S = entropy).

Each of these quantities are more simply represented as functions of pressure, volume, temperature, and entropy as follows:

U = U(S,V),

H = H(S,P),

A = A(T,V),

G = G(T,P),

Gibbs energy has a special place in the area of phase equilibria, because in most first order phase transitions the temperature and pressure of the materials are relatively constant (and therefore the Gibbs energy becomes constant between both phases). The relation of phases between one another can most generally be performed by equating a term called fugacity of each phase. This term (fugacity) is not a very easy term to define, but it can be described as a departure from ideality in Gibbs energy of a phase. It is physically defined as f(fugacity) = P exp( (G - G(i.g.)) / RT ), where G is the real Gibbs energy of the system, G(i.g.) is the ideal gas Gibbs energy (where PV=RT, note: V is specific volume = total volume/n), R is the ideal gas law constant (8.314 J/mol K, 0.00821 liter atm/mol K, 1.987 cal/mol K, 1.986 BTU/lb-mol F), and T is temperature. The idea behind a departure from ideality comes about from the fact that most systems can not be accurately described by the ideal gas formula. The ideal gas formula assumes that molecules in a gas are noninteracting, point particles with completely elastic collisions, but it has been proven with susbsequent equations of state that there are many departures from this ideality introduced in terms which take into account excluded volume of particles, and interaction between particles. One the easier equations of state to add these nonidealities is that of Van der Waals:

P = RT/(V - b) - a/(V^2) Instead of the simple P = RT/V, there are parameters a and b to consider. The parameter a generally represents the interaction between particles and b represents the excluded volume of particles, and it is these type of more complicated equations of state which begin to take into account the real properties of various fluids (Note: with the ideal gas law, only the gas phase is taken into account, but with the more complex equations the liquid phase is able to be described as well). So returning to the description of fugacity, the difference between real Gibbs energy and ideal gas Gibbs energy are used in its definition, and to obtain a real Gibbs energy either a more complex equation of state is required or the application of real experimental data. So if one was working in an ideal gas state (or using ideal gas law as their real Gibbs expression) the terms in the exponential of the fugacity expression would go to zero, and fugactiy would end up just equaling the pressure of the system.

(more to follow soon...)

I'll move it here for the time being; until it gets cleaned and move into sepearte articles, e.g. Gibbs free energy discussion goes in chemical thermodynamics. Later: -- Sadi Carnot 15:25, 2 December 2006 (UTC) reply